Analysis of a Discrete-Time Fractional Order SIR Epidemic Model for Childhood Diseases

  • Mahmoud A. M. AbdelazizEmail author
  • Ahmad Izani Ismail
  • Farah A. Abdullah
  • Mohd Hafiz Mohd
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 295)


In this paper, a discrete-time fractional order SIR epidemic model for a childhood disease with constant vaccination program is investigated. The local asymptotic stability and bifurcation of the equilibrium points are analyzed using basic reproduction number. Flip and Neimark-Sacker (N-S) bifurcations are investigated for endemic equilibrium point and numerical simulations are carried out to illustrate the dynamical behaviors of the model. Chaos phenomenon is observed through numerical simulation inside the flip and N-S bifurcation regions. Results of the numerical simulations support the theoretical analysis.


Discrete-time SIR epidemic model with fractional-order Childhood diseases Vaccination rate Basic reproduction number Flip bifurcation Neimark-Sacker bifurcation Chaos 



The authors would like to thank the editor and the referees for their helpful comments and suggestions.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Mahmoud A. M. Abdelaziz
    • 1
    Email author
  • Ahmad Izani Ismail
    • 1
  • Farah A. Abdullah
    • 1
  • Mohd Hafiz Mohd
    • 1
  1. 1.School of Mathematical Sciences, Universiti Sains MalaysiaPenangMalaysia

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